The following relates to the optoelectronic arts. It especially relates to electrically tunable or adjustable liquid crystal devices, methods of making same, methods of tuning or adjusting same, and devices or apparatuses using same. However, the following will also find application in conjunction with other apparatuses, articles of manufacture, and methods.
There is substantial interest in non-mechanical devices for tunable or adjustable manipulation of light. For example, tunable beam steering devices that can steer a beam of light along different angles or directions responsive to an electrical control input have numerous applications in optics, optical systems, electrooptical systems, and so forth.
Liquid crystal (LC) diffractive devices, such as switchable LC prisms, LC optical phased arrays (OPA), and so forth, are known. These devices typically generate a linear change of optical path delay (OPD) across the aperture, which tilts the phase front and thereby steers the optical beam. The steering angle is related to the magnitude of phase gradient caused by the spatially varying retardation Δn·d where Δn is the effective birefringence and d is the LC cell thickness.
Some known LC beam steering concepts are based on switchable LC prisms using the OPA technology. For a given light wavelength, a phase factor of 2π, corresponding to an OPD of one wavelength, can be periodically subtracted from the phase front without influencing the far-field pattern produced by the phase front.
Problematically, in these approaches it is difficult to achieve a large gradient over a large aperture with a continuous phase profile. A large cell thickness is typically used to achieve a large gradient, but the large cell thickness leads to slow response, absorption, light scattering, or other performance degradation.
In some devices, so-called “resets” are incorporated into the phase profile, the resets having an OPD step that is an integer number of wavelengths of the light. In devices it is known that resets substantially degrade the device efficiency. Such optically phased arrays generally do not provide a sufficiently large steering angle with high efficiency for many applications.
Another known approach is based on a quarter-wave/half-wave/quarter-wave (i.e., “QHQ”) configuration. In this approach, the retardation is designed to be spatially uniform, but the saw-tooth phase profile is implemented by distributing azimuthal angles of LC director configuration. A typical QHQ stack includes an input polarizer, an input quarter-wave plate, a half-wave plate, an output quarter-wave plate, and an output polarizer, in that order. The incident light is processed by the combination of the input polarizer and input quarter-wave to generate circularly polarized input light Ein according to the following Jones matrix-based expression:
                              E          in                =                              [                                                                                Ex                                          i                      ⁢                      n                                                                                                                                        Ey                                          i                      ⁢                      n                                                                                            ]                    =                                    [                                                                                          Ex                                              i                        ⁢                        n                                                                                                                                                        i                      ·                                              Ex                        in                                                                                                        ]                        .                                              (        1        )            In Equation (1), for convenience a right hand circular polarized light convention is used. The symbols Exin, and Eyin represent are vector components along x- and y-axis directions, respectively. The circularly polarized light Ein is input to the half-wave plate to generate output light denoted Eout represented as follows:
                                          E            out                    =                      R            ·            P            ·                          R                              -                1                                      ·                          [                                                                                          Ex                                              i                        ⁢                        n                                                                                                                                                        Ey                                              i                        ⁢                        n                                                                                                        ]                                      ,                            (        2        )            where R and P are Jones matrices for a rotation and a half-wave plate, respectively, and β denotes the angle between the slow axis of the half-wave plate and the x-axis. Equation (2) can be written as:
                                          E            out                    =                                    [                                                                                          cos                      ⁡                                              (                        β                        )                                                                                                                        -                                              sin                        ⁡                                                  (                          β                          )                                                                                                                                                                                sin                      ⁡                                              (                        β                        )                                                                                                                        cos                      ⁡                                              (                        β                        )                                                                                                        ]                        ·                          [                                                                    1                                                        0                                                                                        0                                                                              ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                        φ                                                                                                        ]                        ·                          [                                                                                          cos                      ⁡                                              (                        β                        )                                                                                                                        sin                      ⁡                                              (                        β                        )                                                                                                                                                        -                                              sin                        ⁡                                                  (                          β                          )                                                                                                                                                cos                      ⁡                                              (                        β                        )                                                                                                        ]                        ·                          [                                                                                          Ex                                              i                        ⁢                        n                                                                                                                                                        i                      ·                                              Ex                        in                                                                                                        ]                                      ,                            (        3        )            where φ denotes the phase retardation of the half-wave plate, which is φ=π radians for a half-wave plate. Equation (3) can be written as:
                              E          out                =                                  ⁢                              [                                                                                                                              cos                        2                                            ⁡                                              (                        β                        )                                                              +                                                                  ⅇ                                                  ⅈ                          ⁢                                                                                                          ⁢                          φ                                                                    ·                                                                        sin                          2                                                ⁡                                                  (                          β                          )                                                                                                                                                                                                        cos                        ⁡                                                  (                          β                          )                                                                    ·                                              sin                        ⁡                                                  (                          β                          )                                                                                      ⁢                                          (                                              1                        -                                                  ⅇ                                                      ⅈ                            ⁢                                                                                                                  ⁢                            φ                                                                                              )                                                                                                                                                                                      cos                        ⁡                                                  (                          β                          )                                                                    ·                                              sin                        ⁡                                                  (                          β                          )                                                                                      ⁢                                          (                                              1                        -                                                  ⅇ                                                      ⅈ                            ⁢                                                                                                                  ⁢                            φ                                                                                              )                                                                                                                                                          sin                        2                                            ⁡                                              (                        β                        )                                                              +                                                                  ⅇ                                                  ⅈ                          ⁢                                                                                                          ⁢                          φ                                                                    ·                                                                        cos                          2                                                ⁡                                                  (                          β                          )                                                                                                                                          ]                    ·                                    [                                                                                                                  Ex                                                  i                          ⁢                          n                                                                    ·                                              ⅇ                                                                              ⅈ                            ·                            2                                                    ⁢                                                                                                          ⁢                          β                                                                                                                                                                                                        -                        i                                            ·                                              Ex                                                  i                          ⁢                          n                                                                    ·                                              ⅇ                                                                              ⅈ                            ·                            2                                                    ⁢                                                                                                          ⁢                          β                                                                                                                                ]                        .                                              (        4        )            From Equation (4) it is seen that the output light Eout is left hand circularly polarized light (for input right hand circularly polarized light) with a phase factor ei·2β that depends upon the angle β between the slow axis of the half-wave plate and the x-axis. The output quarter-wave plate and output polarizer serve to convert the final output light back into linearly polarized light, e.g. of the form
         [                                                      Ex              out                        ·                          ⅇ                                                ⅈ                  ·                  2                                ⁢                                                                  ⁢                β                                                                          0                      ]  for output light polarized parallel to the x-axis.
Based on Equation (4), the phase of the transmitted light can be controlled by the azimuthal angle β of the slow axis of the half-wave plate. If the half-wave plate is implemented as a liquid crystal cell, then the angle β and hence the phase of the output light can be varied spatially across the LC cell. If a LC cell has an in-plane or horizontal director configuration in which the in-plane azimuthal angle of the directors linearly rotate from 0 to π across an aperture of the LC cell, and the optical path delay (OPD) everywhere across the cell aperture is π radians corresponding to a half-wave retardation (for the designed wavelength), then the final spatial phase profile of transmitted light Eout will linearly change from 0 to 2π due to the phase factor ei·2β in Equation (4), which has the effect of redirecting or bending the light by an amount controlled by the spatial distance over which the 0 to 2π variation occurs.
LC-based optical elements having the described configuration, that simulate gratings or prisms to redirect or bend light by a selected angle have been fabricated. However, these LC-based optical elements are not continuously tunable or adjustable. Heretofore, LC optical beam-bending or beam-redirecting elements have achieved the spatial variation in in-plane director orientation using static alignment techniques that generate a fixed spatial distribution of the in-plane azimuthal orientation of the LC director across the LC cell. For example, the substrates of the cell can include alignment layers that strongly anchor the LC directors to the desired spatial distribution of azimuthal angles. As a result, the director configuration is fixed when no voltage is applied, and the devices are not tunable. In contrast, in some existing devices an applied voltage can change the steering angle between two or three discrete predetermined angles, but the these devices are not tunable in the sense that the steering angle can be controlled to be one of a large number of angles.
The following contemplates improved assemblies and methods that overcome the above-mentioned limitations and others.